Hi there. Hi have in cylindrical coordinates that , and I must make the graph, and take it into cartesian coordinates. How should I do?

I've tried this way:

I think its a semi-plane parallel to the line: . I thought of working geometrically with it, taking another point. Or taking three points, but I think its probably easier someway, just from the equations system. I don't know how to take x and y, to make them a function of z.

Bye there!

Aug 30th 2010, 09:37 AM

AllanCuz

Quote:

Originally Posted by Ulysses

Hi there. Hi have in cylindrical coordinates that , and I must make the graph, and take it into cartesian coordinates. How should I do?

I've tried this way:

I think its a semi-plane parallel to the line: . I thought of working geometrically with it, taking another point. Or taking three points, but I think its probably easier someway, just from the equations system. I don't know how to take x and y, to make them a function of z.

So, I must use the fact of that its a plane parallel to that line, and work geometrically to get it into a function of z, right?

Aug 30th 2010, 10:00 AM

Ackbeet

It'll be a semi-plane if you're prohibiting negative r-values, and a full plane if you're allowing negative r-values. Polar coordinates usually allow negative r-values. By extension, then, I would think cylindrical coordinates would usually allow negative r-values.

Aug 30th 2010, 04:34 PM

AllanCuz

Quote:

Originally Posted by Soroban

Hello, Ulysses!

Your work is correct . . . just put it together.

. .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

By the way . . .

. . \frac{2}{3} produces: .

. . \dfrac{2}{3} produces: .

Note how this corresponds to the special triangles noted above.

The angle is given by the triangle with the sides , and with the hypotenuse .